CAIE M1 2011 June — Question 4

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2011
SessionJune
TopicMotion on a slope

4 A block of mass 11 kg is at rest on a rough plane inclined at \(30 ^ { \circ }\) to the horizontal. A force acts on the block in a direction up the plane parallel to a line of greatest slope. When the magnitude of the force is \(2 X \mathrm {~N}\) the block is on the point of sliding down the plane, and when the magnitude of the force is \(9 X \mathrm {~N}\) the block is on the point of sliding up the plane. Find
  1. the value of \(X\),
  2. the coefficient of friction between the block and the plane.